so what did you grow in the bowls? do you just leave the table out like a christmas tree?

The table is an ancient tradition with symbolic items displayed. It serves Norooz, as you correctly guessed, as a Christmas tree serves Christmas. It's called the "Haft Seen" (Seven "S's"table). The symbolic meanings are lost through the ages but there are quite reliable guesswork out there that make traditional sense. This one is just as good as any:

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The table is an ancient tradition with symbolic items displayed. It serves Norooz, as you correctly guessed, as a Christmas tree serves Christmas. It's called the "Haft Seen" (Seven "S's"table). The symbolic meanings are lost through the ages but there are quite reliable guesswork out there that make traditional sense. This one is just as good as any: